Unbounded asymptotic equivalences of operator nets with applications

Erkurşun-Özcan N., Gezer N. A.

Positivity, vol.23, no.4, pp.829-851, 2019 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 23 Issue: 4
  • Publication Date: 2019
  • Doi Number: 10.1007/s11117-018-0640-z
  • Journal Name: Positivity
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.829-851
  • Keywords: Unbounded convergence, Asymptotic equivalence, Operator nets
  • TED University Affiliated: No


Present paper deals with applications of asymptotic equivalence relations on operator nets. These relations are defined via unbounded convergences on vector lattices. Given two convergences c and d on a vector lattice, we study d-asymptotic properties of operator nets formed by c-continuous operators. Asymptotic equivalences are known to be useful and extremely important tools to study infinite behaviors of strongly convergent operator nets and continuous semigroups. After giving a general theory, paper focuses on d-martingale and d-Lotz–Räbiger nets.